top of page

Completing the Square

Why?

An equation in vertex form gives us the vertex of a parabola, the direction of opening, and a lot more information. An equation in standard form tells us almost nothing. So how can we go from standard form to vertex form?

 

By completing the square!

Steps

Step 1: Group the x^2 and the x terms together.

 

Step 2: Common factor only the constant terms, if posssible. 

 

Step 3: Complete the square.

 

Step 4: Write it as a binomial squared.

Example:

y= 4x^2 + 16x + 3

y= (4x^2 + 16x) + 3

y= 4(x^2 + 4x) + 3

y= 4(x^2 + 4x + 4 - 4) + 3                      -> There needs to be one positive and one negative                                                                     number to balance each other out                  

 

                  4  ^2

                  2

y= 4[(x^2 + 4x + 4) - 4] + 3

y= 4 (x+2)^2 - 4 + 3

y= 4 (x+2)^2 - 1

 

The vertex is (-2, -1)

Extra Help:

credits to KhanAcademy

bottom of page